A (10 %) rich mixture of heptane (left(mathrm{C}_{7} mathrm{H}_{16} ight)) and air is trapped in the cylinder

A \(10 \%\) rich mixture of heptane \(\left(\mathrm{C}_{7} \mathrm{H}_{16}\right)\) and air is trapped in the cylinder of an engine at a pressure of \(1 \mathrm{bar}\) and temperature of \(400 \mathrm{~K}\). This is compressed and ignited, and at a particular instant during the expansion stroke, when the volume is \(20 \%\) of the trapped volume, the pressure is \(27.06 \mathrm{bar}\). Assuming that the mixture is in chemical equilibrium and contains only \(\mathrm{CO}_{2}, \mathrm{CO}, \mathrm{H}_{2} \mathrm{O}, \mathrm{H}_{2}\) and \(\mathrm{N}_{2}\), find the temperature and molar fractions of the constituents. This solution presupposes that there is no \(\mathrm{O}_{2}\) in the products; use your results to confirm this.

[2000 K; 0.1037; 0.0293; 0.1434; 0.00868; 0.7148]